Advertisements
Advertisements
प्रश्न
If `x/a = y/b = z/c`, prove that `x^3/a^2 + y^3/b^2 + z^3/c^2 = (x+ y+ z)^3/(a + b+ c)^2`
Advertisements
उत्तर
`x/a = y/b = z/c`
∴ x = ak, y = bk, z = ck
L.H.S. = `x^3/a^2 + y^3/b^2 + z^3/c^2`
= `(a^3k^3)/a^2 + (b^3k^3)/(b^2) + (c^3k^3)/c^2`
= ak3 + bk3 + ck3
= k3(a + b + c)
R.H.S. = `(x + y + z)^3/(a + b + c)^2`
= `(ak + bk + ck)^3/(a + b + c)^2`
= `(k^3(a + b + c)^3)/((a + b + c)`
= k3(a + b + c)
Hence L.H.S. = R.H.S.
APPEARS IN
संबंधित प्रश्न
Find the fourth proportional to 1.5, 4.5 and 3.5
If a, b, c are in continued proportion, show that: `(a^2 + b^2)/(b(a + c)) = (b(a + c))/(b^2 + c^2)`.
If a, b and c are in continued proportion, prove that: a: c = (a2 + b2) : (b2 + c2)
If ax = by = cz, prove that
`x^2/(yz) + y^2/(zx) + z^2/(xy) = (bc)/a^2 + (ca)/b^2 + (ab)/c^2`.
If a, b, c, d are in continued proportion, prove that:
`sqrt(ab) - sqrt(bc) + sqrt(cd) = sqrt((a - b + c) (b - c + d)`
Verify the following:
108 : 72 : : 129 : 86
Write (T) for true and (F) for false in case of the following:
45 km : 60 km : : 12 h : 15 h
If 25 : 35 : : 45 : x, then the value of x is
If 2, 6, p, 54 and q are in continued proportion, find the values of p and q.
The shadow of a 3 m long stick is 4 m long. At the same time of the day, if the shadow of a flagstaff is 24 m long, how tall is the flagstaff?
